1. Field of the Invention
The present invention relates to a pattern recognition technique that uses a computer to judge to which of plural categories an input image and other data belong.
2. Description of the Related Art
Conventionally, pattern recognition methods by use of a computer have been proposed. For example, the following research is conducted. The image of a human face captured by an image sensor is analyzed to judge which portions of the image correspond to an eye, a nose, and other features, to categorize the portions/features and to determine to whose face the image corresponds by comparing the image with categorized images stored in advance.
A subspace method is well known as a pattern recognition method. According to the subspace method, a subspace is defined for each of plural categories, and by determining with which subspace an unknown pattern has the highest degree of relation, a category to which the unknown pattern belongs is determined. In the subspace method, where there are many categories, recognition accuracy becomes low, and it also becomes low for nonlinear pattern distributions.
Another well-known recognition method is the support vector machine (SVM) method. In the SVM method, by introducing a kernel function, low-dimension patterns are turned into high-dimension patterns, and nonlinear pattern distributions can also be recognized. However, the number of categories to which the method is applied is no more than two and an enormous amount of computation is required.
Recently, the kernel nonlinear subspace method has been proposed, which combines the advantages of the subspace method and the advantages of the SVM method (Japanese Published Unexamined Patent Application No. 2000-90274). In the kernel nonlinear subspace method, patterns to be recognized are mapped to a high-dimension nonlinear space using nonlinear conversion definable by a kernel function to create high-dimension patterns, as in the SVM method, and pattern recognition is performed by applying the subspace method on the high-dimension nonlinear space.
The kernel nonlinear subspace method, to define a subspace of a category “i” creates base vectors by linear combination of mappings of all learning samples to a nonlinear space. Herein, as a method of calculating an evaluation value for judging whether an unknown input pattern belongs to a category, a method is disclosed which utilizes projection components produced when a pattern to be recognized is projected to subspaces on a high-dimension liner space that correspond to categories. Since the subspaces are defined by linearly combining base vectors produced using learning samples, which are low-dimension vectors, the projection components to be obtained to recognize input patterns can be calculated simply by calculating the low-dimension vectors by use of a kernel function.
However, since the computation includes kernel operations between the pattern to be recognized and all learning samples, and inner product operations with the number of all learning sample as a dimension count, when the number of learning samples increases, the amount of computation would increase in proportion to the number of learning samples. Moreover, since all learning samples must be saved for kernel computation, there has been a problem in that a large storage area is required.
Since a learning process is performed by singular value decomposition of a kernel matrix with the results of kernel operations between learning samples as components, there is a problem in that, when a learning sample is newly added, learning must be performed again using existing learning samples to recalculate the weight of linear combination of base vectors constituting a subspace.
A kernel function must have been selected beforehand for recognition targets and cannot be adaptively changed depending on learning, posing the problem that recognition accuracy does not increase.